Difference between revisions of "Whittaker transform"
From Encyclopedia of Mathematics
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The integral transform | The integral transform | ||
| − | $$F(x)=\int\limits_0^\infty(2xt)^{-1/4}W_{\lambda,\mu}(2xt)f(t)dt,$$ | + | $$F(x)=\int\limits_0^\infty(2xt)^{-1/4}W_{\lambda,\mu}(2xt)f(t)\,dt,$$ |
where $W_{\lambda,\mu}(z)$ is the Whittaker function (cf. [[Whittaker functions|Whittaker functions]]). For $\lambda=1/4$ and $\mu=\pm1/4$ the Whittaker transform goes over into the [[Laplace transform|Laplace transform]]. | where $W_{\lambda,\mu}(z)$ is the Whittaker function (cf. [[Whittaker functions|Whittaker functions]]). For $\lambda=1/4$ and $\mu=\pm1/4$ the Whittaker transform goes over into the [[Laplace transform|Laplace transform]]. | ||
Revision as of 14:30, 14 February 2020
The integral transform
$$F(x)=\int\limits_0^\infty(2xt)^{-1/4}W_{\lambda,\mu}(2xt)f(t)\,dt,$$
where $W_{\lambda,\mu}(z)$ is the Whittaker function (cf. Whittaker functions). For $\lambda=1/4$ and $\mu=\pm1/4$ the Whittaker transform goes over into the Laplace transform.
References
| [1] | C.S. Meijer, "Eine neue Erweiterung der Laplace-Transformation" Proc. Koninkl. Ned. Akad. Wet. , 44 (1941) pp. 727–737 |
Comments
References
| [a1] | G. Doetsch, "Handbuch der Laplace-Transformation" , III , Birkhäuser (1973) |
| [a2] | E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1927) |
How to Cite This Entry:
Whittaker transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Whittaker_transform&oldid=32643
Whittaker transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Whittaker_transform&oldid=32643
This article was adapted from an original article by Yu.A. BrychkovA.P. Prudnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article